Asymmetric Yield Effect Evolving With Internal Variables During Continuous Large Deformations And Its FEM Validation

In hexagonal close-packed(HCP)metals and their alloys,the asymmetric yielding effect that strongly evolves with internal variables is very significant during continuous large deformation processes,which has a significant impact on forming properties,which limits the engineering applications of hexagonal close-packed metals and their alloys.The important scientific problems of quantitatively corresponding to the microstructure and texture evolution of macroscopic properties are brought up.In this study,a powerful stress-invariant-asymmetric-yield function capable of accurately describing the hydrostatic pressure sensitivity(HPS),tension-compression strength differential effect(SDE),and anisotropy is applied.An analytical interpolation method based on a function that takes into account internal variables and a Lode parameter of stress state was developed to establish a continuous evolution between adjacent yield surfaces.A rate-independent large deformation hypoelasto-plastic constitutive relationship with adequately consideration of asymmetric yield evolution is constructed.A plastic potential for the non-associated flow rule is introduced to eliminate the plastic dilatancy.The plastic modulus is modified by the partial derivative of the continuous interpolation yield function that can capture the evolutionary effect on the internal variables,and the plastic modulus is analytically and simply expressed.The asymmetric yielding effect and constitutive description of the evolution were numerically verified.Finite element simulations of thickness compression and in-plane compression Zr under continuous large deformation conditions were performed using an explicit integration algorithm.The calculation results have small errors and high calculation efficiency.The results show that:(1)For the different levels of pre-strain,the continuously interpolated asymmetric yield function,together with the proposed constitutive relationship,can precisely describe the non-evolving asymmetric yield of HCP-structured Zr as the traditional ones^[1,2]without considering the evolution effect.(2)For continuous large deformation loading,the stress-invariant-asymmetric-yield function together with the proposed continuous interpolation and large deformation constitutions,considering the evolution effect,jointly and clearly corrects the strain hardening rates for all loading routes,and the corrected simulations are in better agreement with the theoretical stress-strain data than uncorrected simulations,in particular for the routes along which the yield surfaces clearly evolve.(3)In the process of continuous large deformation,the in-plane compression Zr exhibits a stronger asymmetric yielding effect with cumulative plastic strain evolution than the thickness compression Zr,the continuous interpolation yield function and large deformation constitutive relationship considering the evolution effect can still be accurately described the strain hardening rate and the stress-strain relationship can accurately capture the softening effect on the biaxial tensile path of in-plane compression Zr.However,the traditional yield function does not take into account the hydrostatic pressure correlation,the asymmetry of tension and compression,the anisotropy,and their evolution,so it cannot capture the softening effect,and the traditional yield function is not suitable for describing the large deformation asymmetric yield process.The asymmetric yield evolution and its large deformation constitutive description proposed in this paper have high accuracy and wide applicability,and are suitable for a variety of single or multiple internal variable asymmetric yield and nonlinear plastic behavior of complex loading paths.It can be used for precision engineering simulation of HCP metals and their alloys and scientific research of corresponding microscopic mechanisms.